Algebra Item Sampler 2018 - Radnor Township School DistrictKeystone Algebra I Item and Scoring...

Pennsylvania Department of Education Bureau of Curriculum, Assessment and Instruction—September 2018

Algebra I

Item and Scoring Sampler

2018

PennsylvaniaKeystone Exams

Keystone Algebra I Item and Scoring Sampler—September 2018 ii

TABLE OF CONTENTS

INFORMATION ABOUT ALGEBRA IIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1About the Keystone Exams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Depth of Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Exam Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Item and Scoring Sampler Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Algebra I Exam Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4General Description of Scoring Guidelines for Algebra I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Formula Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ALGEBRA I MODULE 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Multiple-Choice Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Constructed-Response Item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Constructed-Response Item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Algebra I Module 1—Summary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

ALGEBRA I MODULE 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Multiple-Choice Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Constructed-Response Item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Constructed-Response Item . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Algebra I Module 2—Summary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Keystone Algebra I Item and Scoring Sampler—September 2018 1

INFORMATION ABOUT ALGEBRA I

INTRODUCTION

General Introduction

The Pennsylvania Department of Education (PDE) provides districts and schools with tools to assist in delivering focused instructional programs aligned to the Pennsylvania Core Standards. These tools include the standards, assessment anchor documents, Keystone Exams Test Definition, Classroom Diagnostic Tool, Standards Aligned System, and content-based item and scoring samplers. This 2018 Algebra I Item and Scoring Sampler is a useful tool for Pennsylvania educators in preparing students for the Keystone Exams.

This Item and Scoring Sampler contains released operational multiple-choice and constructed-response items that have appeared on previously administered Keystone Exams. These items will not appear on any future Keystone Exams. Released items provide an idea of the types of items that have appeared on operational exams and that will appear on future operational Keystone Exams. Each item has been through a rigorous review process to ensure alignment with the Assessment Anchors and Eligible Content. This sampler includes items that measure a variety of Assessment Anchor or Eligible Content statements, but it does not include sample items for all Assessment Anchor or Eligible Content statements.

The items in this sampler may be used as examples for creating assessment items at the classroom level and may also be copied and used as part of a local instructional program.1 Classroom teachers may find it beneficial to have students respond to the constructed-response items in this sampler. Educators can then use the sampler as a guide to score the responses either independently or together with colleagues.

This Item and Scoring Sampler is available in Braille format. For more information regarding Braille call (717)-901-2238.

ABOUT THE KEYSTONE EXAMS

The Keystone Exams are end-of-course assessments currently designed to assess proficiencies in Algebra I, Biology, and Literature. For detailed information about how the Keystone Exams are being integrated into the Pennsylvania graduation requirements, please contact the Pennsylvania Department of Education or visit the PDE website at http://www.education.pa.gov.

Alignment

The Algebra I Keystone Exam consists of exam questions grouped into two modules: Module 1—Operations and Linear Equations & Inequalities, and Module 2—Linear Functions and Data Organizations. Each module corresponds to specific content, aligned to statements and specifications included in the course-specific assessment anchor documents. The Algebra I content included in the Keystone Algebra I multiple-choice items will align with the Assessment Anchors as defined by the Eligible Content statements. The process skills, directives, and action statements will also specifically align with the Assessment Anchors as defined by the Eligible Content statements.

The content included in Algebra I constructed-response items aligns with content included in the Eligible Content statements. The process skills, directives, and action statements included in the performance demands of the Algebra I constructed-response items align with specifications included in the Assessment Anchor statements, the Anchor Descriptor statements, and/or the Eligible Content statements. In other words, the verbs or action statements used in the constructed-response items or stems can come from the Eligible Content, Anchor Descriptor, or Assessment Anchor statements.

1 The permission to copy and/or use these materials does not extend to commercial purposes.



Depth of Knowledge

Webb’s Depth of Knowledge (DOK) was created by Dr. Norman Webb of the Wisconsin Center for Education Research. Webb’s definition of depth of knowledge is the cognitive expectation demanded by standards, curricular activities, and assessment tasks. Webb’s DOK includes four levels, from the lowest (basic recall) level to the highest (extended thinking) level.

Depth of KnowledgeLevel 1 RecallLevel 2 Basic Application of Skill/ConceptLevel 3 Strategic ThinkingLevel 4 Extended Thinking

Each Keystone item has been through a rigorous review process and is assigned a DOK level. For additional information about depth of knowledge, please visit the PDE website at http://static.pdesas.org/Content/Documents/Keystone_Exam_Program_Overview.pdf.

Exam Format

The Keystone Exams are delivered in a paper-and-pencil format as well as in a computer-based online format. The multiple-choice items require students to select the best answer from four possible answer options and record their answers in the spaces provided. The correct answer for each multiple-choice item is worth one point. The constructed-response items require students to develop and write (or construct) their responses. Constructed-response items in Algebra I are scored using item-specific scoring guidelines based on a 0–4-point scale. Each multiple-choice item is designed to take about one to one-and-a-half minutes to complete. Each constructed-response item is designed to take about 10 minutes to complete. The estimated time to respond to a test question is the same for both test formats. During an actual exam administration, students are given additional time as necessary to complete the exam.



ITEM AND SCORING SAMPLER FORMAT

This sampler includes the test directions, scoring guidelines, and formula sheet that appear in the Keystone Exams. Each sample multiple-choice item is followed by a table that includes the alignment, the answer key, the DOK, the percentage2 of students who chose each answer option, and a brief answer option analysis or rationale. Each constructed-response item is followed by a table that includes the alignment, the DOK, and the mean student score. Additionally, each of the included item-specific scoring guidelines is combined with sample student responses representing each score point to form a practical, item-specific scoring guide. The General Description of Scoring Guidelines for Algebra I used to develop the item-specific scoring guidelines should be used if any additional item-specific scoring guidelines are created for use within local instructional programs.

Example Multiple-Choice Item Information Table

Item Information

Alignment Assigned AAEC

Answer Key Correct Answer

Depth of Knowledge Assigned DOK

p-value A Percentage of students who selected each option

p-value B Percentage of students who selected each option

p-value C Percentage of students who selected each option

p-value D Percentage of students who selected each option

Option Annotations Brief answer option analysis or rationale

Example Constructed-Response Item Information Table

Alignment Assigned AAEC Depth of Knowledge

Assigned DOK Mean Score

2 All p-value percentages listed in the item information tables have been rounded.



ALGEBRA I EXAM DIRECTIONS

Directions:

Below are the exam directions available to students. These directions may be used to help students navigate through the exam.

Formulas that you may need to solve questions in this module are found on page 7 of this test booklet. You may refer to the formula page at any time during the exam.

You may use a calculator on this module. When performing operations with π (pi), you may use either calculator π or the number 3.14 as an approximation of π.

There are two types of questions in each module.

Multiple-Choice Questions:

These questions will ask you to select an answer from among four choices.

• First read the question and solve the problem on scratch paper. Then choose the correct answer.

• Only one of the answers provided is correct.

• If none of the choices matches your answer, go back and check your work for possible errors.

• Record your answer in the Algebra I answer booklet.

Constructed-Response Questions:

These questions will require you to write your response.

• These questions have more than one part. Be sure to read the directions carefully.

• You cannot receive the highest score for a constructed-response question without completing all the tasks in the question.

• If the question asks you to show your work or explain your reasoning, be sure to show your work or explain your reasoning. However, not all questions will require that you show your work or explain your reasoning. If the question does not require that you show your work or explain your reasoning, you may use the space provided for your work or reasoning, but the work or reasoning will not be scored.

• All responses must be written in the appropriate location within the response box in the Algebra I answer booklet. Some answers may require graphing, plotting, labeling, drawing, or shading. If you use scratch paper to write your draft, be sure to transfer your final response to the Algebra I answer booklet.



If you finish early, you may check your work in Module 1 [or Module 2] only.

y Do not look ahead at the questions in Module 2 of your exam materials. y After you have checked your work, close your exam materials.

You may refer to this page at any time during this portion of the exam.



GENERAL DESCRIPTION OF SCORING GUIDELINES FOR ALGEBRA I

4 Points

• The response demonstrates a thorough understanding of the mathematical concepts and procedures required by the task.

• The response provides correct answer(s) with clear and complete mathematical procedures shown and a correct explanation, as required by the task. Response may contain a minor “blemish” or omission in work or explanation that does not detract from demonstrating a thorough understanding.

3 Points

• The response demonstrates a general understanding of the mathematical concepts and procedures required by the task.

• The response and explanation (as required by the task) are mostly complete and correct. The response may have minor errors or omissions that do not detract from demonstrating a general understanding.

2 Points

• The response demonstrates a partial understanding of the mathematical concepts and procedures required by the task.

• The response is somewhat correct with partial understanding of the required mathematical concepts and/or procedures demonstrated and/or explained. The response may contain some work that is incomplete or unclear.

1 Point

• The response demonstrates a minimal understanding of the mathematical concepts and procedures required by the task.

0 Points

• The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures required by the task.

Special Categories within zero reported separately:

Blank .....................................Blank, entirely erased, entirely crossed out, or consists entirely of whitespace

Refusal ..................................Refusal to respond to the task

Off Task .................................Makes no reference to the item but is not an intentional refusal

Foreign Language ................Written entirely in a language other than English

Illegible .................................Illegible or incoherent



FORMULA SHEET

Formulas that you may need to solve questions on this exam are found below. You may use calculator π or the number 3.14 as an approximation of π.

A lw

l

w

V lwh

Arithmetic Properties

Additive Inverse: a ( a) 0

Multiplicative Inverse: a 1

Commutative Property: a b b a a b b a

Associative Property: (a b) c a (b c) (a b) c a (b c)

Identity Property: a 0 a a 1 a

Distributive Property: a (b c) a b a c

Multiplicative Property of Zero: a 0 0

Additive Property of Equality:If a b, then a c b c

Multiplicative Property of Equality:If a b, then a c b c

1a

Linear Equations

Slope: m

Point-Slope Formula: (y y 1) m(x x 1)

Slope-Intercept Formula: y mx b

Standard Equation of a Line: Ax By C

y 2 y 1x 2 x 1

FORMULA SHEETALGEBRA I


1Algebra I MODULE 1

ALGEBRA I MODULE 1Multiple-Choice Items

1. Four values are listed below.

1 } 7 20% Ï

} 0.5 |ˉ0.5|

Which list shows the values in order from least to greatest?

A. |ˉ0.5| Ï}

0.5 1 } 7 20%

B. |ˉ0.5| 1 } 7 20% Ï

} 0.5

C. 1 } 7 20% |ˉ0.5| Ï

} 0.5

D. 1 } 7 Ï

} 0.5 |ˉ0.5| 20%

673946

Item Information

Alignment A1.1.1.1.1

Answer Key C

Depth of Knowledge 1

p-value A 14%

p-value B 17%

p-value C 60% (correct answer)

p-value D 9%

Option Annotations A student could determine the correct answer, option C, by converting the numbers to their rational approximations and then ordering the rational approximations from least to greatest.

A student could arrive at an incorrect answer by converting the numbers to an incorrect approximation or by misinterpreting what the numbers represent. For example, a student could arrive at option B by not applying the absolute value bars and treating | ̄ 0.5| as equal to ˉ0.5.


1Algebra I MODULE 1

2. An inequality is shown below.

4(ab)3 > 15a3b

Which values of a and b make the inequality true?

A. a = 1 b = 1

B. a = 1 b = 2

C. a = 2 b = 0

D. a = 2 b = 1

674460

Item Information


Answer Key B


p-value A 11%

p-value B 62% (correct answer)

p-value C 13%

p-value D 14%

Option Annotations A student could determine the correct answer, option B, by simplifying the

inequality to b2 > 15 } 4 and identifying a positive value for b that makes the

simplified inequality true.

A student could arrive at an incorrect answer by incorrectly evaluating the inequality. For example, a student could arrive at option D by substituting 21 for ab on the left-hand side.


1Algebra I MODULE 1

3. An equation involving polynomials is shown below.

(ax + 5y ) + (x – y ) – (3x – by ) = 2x + y

What are the values of a and b?

A. a = 4 b = ˉ3

B. a = 4 b = 3

C. a = 5 b = ˉ5

D. a = 5 b = 5

700845

Item Information


Answer Key A


p-value A 41% (correct answer)

p-value B 31%

p-value C 17%

p-value D 11%

Option Annotations A student could determine the correct answer, option A, by distributing the subtraction through the third binomial, combining like terms, and simplifying the equation to ax + by = 4x + ˉ3y .

A student could arrive at an incorrect answer by incorrectly simplifying the equation. For example, a student could arrive at option B by not distributing the negative symbol across negative by and simplifying the equation involving the y terms to 3y = by .


1Algebra I MODULE 1

4. Simplify:

3x 2 + 3x – 6 }} 6x 2 + 18x + 12

; x ≠ ˉ2, ˉ1

A. 1 } 10

B. 1 } 2

C. x – 1 } 2(x + 1)

D. 2(x – 1)

} x + 1

674455

Item Information


Answer Key C


p-value A 11%

p-value B 22%


p-value D 16%

Option Annotations A student could determine the correct answer, option C, by factoring the numerator to 3(x – 1)(x + 2), factoring the denominator to 6(x + 1)(x + 2), and then canceling out the common factors: 3 and (x + 2).

A student could arrive at an incorrect answer by incorrectly factoring the numerator and/or denominator. For example, a student could arrive at option B by factoring the numerator as 3(x + 1)(x + 2).


1Algebra I MODULE 1

5. Joan has a gym gift card worth $100. Each time she visits the gym, $12 is deducted from the amount remaining on the gift card. Which equation can be used to determine the amount of money (m), in dollars, remaining on the gift card after Joan visits the gym d times?

A. m = 12 – 100d

B. m = 12d – 100

C. m = ˉ12 + 100d

D. m = ˉ12d + 100674501

Item Information


Answer Key D


p-value A 7%

p-value B 39%

p-value C 4%

p-value D 50% (correct answer)

Option Annotations A student could determine the correct answer, option D, by identifying 100 as the initial value, ˉ12 as the rate of change, and that the rate of change should be multiplied by the variable d.

A student could arrive at an incorrect answer by placing the variable with the incorrect value and/or by misidentifying which term should be subtracted. For example, a student could arrive at option B by subtracting the 100 instead of the 12d.


1Algebra I MODULE 1

6. The equation below describes the relationship between the number of months (x ) since a customer began renting a storage unit and the total amount of money (y ), in dollars, the customer has paid to the storage facility.

y = 15x + 30

Which statement describes a solution of the equation based on the number of months the customer has rented the storage unit?

A. After exactly 16 months, the customer has paid $240.

B. After exactly 240 months, the customer has paid $16.

C. After exactly 16 months, the customer has paid $270.

D. After exactly 270 months, the customer has paid $16.700820

Item Information


Answer Key C


p-value A 14%

p-value B 4%


p-value D 2%

Option Annotations A student could determine the correct answer, option C, by identifying (16, 270) as a possible solution, identifying the 16 as the number of months, and identifying the 270 as the amount the customer has paid.

A student could arrive at an incorrect answer by not including the “+ 30” and/or by interpreting the values incorrectly. For example, a student could arrive at option A by using y = 15x but correctly interpreting that 16 represents the number of months.


1Algebra I MODULE 1

7. Charlene owns a bookstore. She purchases used books from customers.

• She pays $3.50 for each hardback book. • She pays $0.75 for each paperback book. • Charlene pays a customer a total of $199.75 for 149 used books.

Which system of equations could be used to determine the number of hardback books (x ) and the number of paperback books (y ) Charlene purchases from the customer?

A. x + y = 199.75 0.75x + 3.50y = 149

B. x + y = 149 0.75x + 3.50y = 199.75

C. x + y = 199.75 3.50x + 0.75y = 149

D. x + y = 149 3.50x + 0.75y = 199.75

700841

Item Information


Answer Key D


p-value A 5%

p-value B 10%

p-value C 12%


Option Annotations A student could determine the correct answer, option D, by identifying that x and y represent the number of books purchased so their sum must be 149 and by identifying that the expression 3.50x represents paying $3.50 for each hardback book and that the expression 0.75y represents paying $0.75 for each paperback book so the sum of these expressions must be 199.75.

A student could arrive at an incorrect answer by switching the total amount paid with the total number of books and/or switching the coefficients for x and y in the second equation. For example, a student could arrive at option C by switching the total amount paid with the total number of books.


1Algebra I MODULE 1

8. Gloria is considering two different movie services.

• Service A charges a $15.00 monthly fee for unlimited streaming of movies and $2.50 per DVD rental.

• Service B charges a $12.00 monthly fee for unlimited streaming of movies and $3.50 per DVD rental.

The system of equations below describes the relationship between the number of DVDs rented per month (x ) and the monthly cost (y ), in dollars, for both services.

y = 15.00 + 2.50x

y = 12.00 + 3.50x

Which statement about the costs of the movie services is true?

A. When Gloria rents 3 DVDs per month, either service will cost her $22.50 per month.

B. When Gloria rents 6 DVDs per month, either service will cost her $27.00 per month.

C. When Gloria rents fewer than 3 DVDs per month, service A will cost less per month than service B will cost.

D. When Gloria rents more than 3 DVDs per month, service B will cost $12 more per month than service A will cost.

700842

Item Information


Answer Key A



p-value B 5%

p-value C 12%

p-value D 6%

Option Annotations A student could determine the correct answer, option A, by determining the solution for the system of equations is (3, 22.50) and interpreting that ordered pair as the point for which both services will cost the same amount.

A student could arrive at an incorrect answer by incorrectly interpreting what the variables represent. For example, a student could arrive at option C by considering only the 2.50 and 3.50 which would lead to Service A always costing less.


1Algebra I MODULE 1

9. An inequality is shown below.

5x – 6 < 4 + 6x

Which is a graph of the solution set of the inequality?

A. –14 –13 –12 –11 –10 –9 –8 –7

B. –14 –13 –12 –11 –10 –9 –8 –7

C. –5 –4 –3 –2 –1 0 1 2

D. –5 –4 –3 –2 –1 0 1 2

640609

Item Information


Answer Key B


p-value A 24%


p-value C 17%

p-value D 13%

Option Annotations A student could determine the correct answer, option B, by correctly solving the inequality for x > ˉ10 and identifying the graph with an open circle at ˉ10 is shaded to the right of the open circle.

A student could arrive at an incorrect answer by reversing the direction of the inequality and/or adding 4 to ˉ6 instead of subtracting the 4 from ˉ6. For example, a student could arrive at option A by reversing the direction of the inequality.


1Algebra I MODULE 1

10. A part for a machine must meet certain length requirements, in centimeters (cm), as shown in the inequality below.

|6.75 – x | < 0.25

Which statement completely describes the length requirements for this machine part?

A. The length of the part must be less than 7 cm.

B. The length of the part must be greater than 6.5 cm.

C. The length of the part must be less than 6.5 cm or greater than 7 cm.

D. The length of the part must be greater than 6.5 cm and less than 7 cm.704000

Item Information


Answer Key D


p-value A 22%

p-value B 20%

p-value C 18%


Option Annotations A student could determine the correct answer, option D, by rewriting the absolute value inequality as the compound inequality ˉ0.25 < 6.75 – x < 0.25, simplifying the inequality to 6.5 < x < 7, and interpreting the inequality to mean x (the length) must be greater than 6.5 and less than 7.

A student could arrive at an incorrect answer by not considering the absolute value bars, misapplying the absolute value bars, and/or misreading the inequality symbol. For example, a student could arrive at option A by switching the terms within the absolute value bars and then solving x – 6.75 < 0.25 as x < 7.


1Algebra I MODULE 1

11. A graph of a system of inequalities is shown below.

x

y

2 4 6 8 10−2−4−6−8−10

−4−6−8

−10

−2

2468

10

Which system of inequalities describes the graph?

A. 4x + 3y > 24 5x + 8y < 40

B. 4x + 3y ≥ 24 5x + 8y ≤ 40

C. 4x + 3y < 24 5x + 8y > 40

D. 4x + 3y ≤ 24 5x + 8y ≥ 40

666554


1Algebra I MODULE 1

Item Information


Answer Key B


p-value A 15%


p-value C 14%

p-value D 24%

Option Annotations A student could determine the correct answer, option B, by identifying both boundaries as solid lines so the inequalities should both be inclusive and determining that the shaded region is above the line 4x + 3y = 24 and below the line 5x + 8y = 40.

A student could arrive at an incorrect answer by reversing the inequalities and/or by using strict (non-inclusive) inequalities. For example, a student could arrive at option D by reversing both inequalities.


1Algebra I MODULE 1

12. All the books in a bookstore window display today will be mysteries and biographies. The system of inequalities below describes the relationship between the number of mysteries (x ) and the number of biographies (y ) that could be in the display.

x + y ≤ 30

2x ≤ 3y

Which description is a possible number of books of each type that could be in the display?

A. 6 mysteries and 22 biographies

B. 15 mysteries and 8 biographies

C. 21 mysteries and 14 biographies

D. 24 mysteries and 12 biographies700855

Item Information


Answer Key A



p-value B 13%

p-value C 13%

p-value D 8%

Option Annotations A student could determine the correct answer, option A, by identifying a pair of numbers that have a sum no greater than 30 such that the number of mysteries is no more than 1.5 times the number of biographies.

A student could arrive at an incorrect answer by satisfying only one of the two inequalities. For example, a student could arrive at option C by identifying a set of values such that the number of mysteries is 1.5 times the number of biographies but does not consider that the total number of books (35) is greater than 30.


1Algebra I MODULE 1

THIS PAGE IS INTENTIONALLY BLANK.


1Algebra I MODULE 1

CONSTRUCTED-RESPONSE ITEM

13. Small baskets of tomatoes are sold at a vegetable stand for $3 per basket. Large baskets of tomatoes are sold at the stand for $5 per basket. Only whole numbers of baskets may be purchased.

A customer purchases a total of 8 baskets of tomatoes and pays $36.

A. Write and solve a system of equations that models the number of small baskets (x ) and the number of large baskets (y ) that the customer purchases. Show or explain all your work.

Go to the next page to finish question 13. GO ON


1Algebra I MODULE 1

13. Continued. Please refer to the previous page for task explanation.

Another customer claims that he can purchase a total of 10 baskets of tomatoes and pay $45.

B. Use a system of equations that describes this other customer’s purchase to explain why the claim is incorrect.

674404

STOPAFTER YOU HAVE CHECKED YOUR WORK, CLOSE YOUR ANSWER BOOKLET AND TEST BOOKLET SO YOUR TEACHER WILL KNOW YOU ARE FINISHED.


1Algebra I MODULE 1

Item-Specific Scoring Guideline

#13 Item Information

Alignment A1.1.2 Depth of Knowledge 2 Mean Score 1.58

Assessment Anchor this item will be reported under:

A1.1.2—Linear Equations

Specific Assessment Anchor Descriptor addressed by this item:

A1.1.2.2—Write, solve, and/or graph systems of linear equations using various methods.

Scoring Guide

Score Description

4 The student demonstrates a thorough understanding of linear equations by correctly solving problems with clear and complete procedures and explanations when required.

3 The student demonstrates a general understanding of linear equations by solving problems and providing procedures and explanations with only minor errors or omissions.

2 The student demonstrates a partial understanding of linear equations by providing a portion of the correct problem solving, procedures, and explanations.

1 The student demonstrates a minimal understanding of linear equations.

0The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question.

Top-Scoring Student Response and Training Notes

Score Description

4 Student earns 4 points.

3 Student earns 3.0–3.5 points.


1Student earns 0.5–1.5 points. OR Student demonstrates minimal understanding of linear equations.

0Response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.


1Algebra I MODULE 1

Top-Scoring Response

Part A (3 points):

1 __ 2

point for each correct equation

1 __ 2

point for each correct value of the solution

OR 1 __ 2 point for embedded solution

1 point for complete support

OR 1 __ 2 point for correct but incomplete support

What? Why?

x + y = 83x + 5y = 36

AND

Sample Work: x + y = 83x + 5y = 36

x = 8 – y 3x + 5y = 36

x = 2 (small baskets)y = 6 (large baskets)

3(8 – y ) + 5y = 3624 – 3y + 5y = 36

→ x + 6 = 8

2y = 12 x = 2y = 6

OR

Sample Explanation:

First, I set up my system of equations.

x + y = 8

3x + 5y = 36

I then multiplied the first row by 5 and the second row by –1, so I

could add them together and cancel out the y -terms. This gave me

2x = 4, so x = 2. I substituted this value into the first equation and

solved it for y to get y = 6.

→


1Algebra I MODULE 1

Part B (1 point):

1 point for correct and complete explanation

OR 1 } 2 point for correct but incomplete explanation

What? Why?

Sample Explanation:

The system of equations that describes this other customer’s purchase is shown.

x + y = 10

3x + 5y = 45

The solution of this system of equations exists, but neither x nor y is a whole number, so the customer cannot purchase 10 baskets of tomatoes for $45.


1Algebra I MODULE 1

STUDENT RESPONSE

Response Score: 4 points

PARTS A AND B

Que

stio

n 13

Page

1

The

stud

ent h

as p

rovi

ded

two

corr

ect

equa

tions

, a c

orre

ct so

lutio

n, a

nd

com

plet

e su

ppor

t.

The

stud

ent h

as p

rovi

ded

a co

rrec

t an

d co

mpl

ete

expl

anat

ion.


1Algebra I MODULE 1

STUDENT RESPONSE






The student has provided one correct equation, a correct solution, and correct but incomplete support.


1Algebra I MODULE 1





The student has provided a correct and complete explanation.


1Algebra I MODULE 1

STUDENT RESPONSE


PARTS A AND B

Que

stio

n 13

Page

1

The

stud

ent h

as p

rovi

ded

no c

orre

ct

equa

tions

, a c

orre

ct so

lutio

n, a

nd c

orre

ct

but i

ncom

plet

e su

ppor

t.

The

stud

ent h

as p

rovi

ded

a co

rrec

t but

inco

mpl

ete

expl

anat

ion.

(The

syst

em o

f equ

atio

ns is

foun

d, b

ut th

ere

is no

exp

lana

tion

why

the

clai

m w

ill n

ot w

ork

for t

his s

yste

m.)


1Algebra I MODULE 1



1Algebra I MODULE 1

STUDENT RESPONSE

Response Score: 1 point





The student has provided one correct equation, an incorrect solution, and incorrect support.


1Algebra I MODULE 1





The student has provided an incorrect explanation.


1Algebra I MODULE 1

STUDENT RESPONSE


PARTS A AND B

Que

stio

n 13

Page

1

The

stud

ent h

as p

rovi

ded

no c

orre

ct

equa

tions

, an

inco

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t sol

utio

n, a

nd

no su

ppor

t.

The

stud

ent h

as p

rovi

ded

an in

corr

ect

expl

anat

ion.


1Algebra I MODULE 1



1Algebra I MODULE 1


14. Kyle has $4 more than twice as much money as Lana. Lana has x dollars. Kyle does not have enough money to buy a video game that costs $56, but he has enough money to buy a textbook that costs $38.

A. Write a compound inequality that represents all the possible amounts of money Kyle could have in terms of x .

compound inequality:

B. What is the least amount of money Lana could have?

$



1Algebra I MODULE 1


Lana has a whole number of dollars.

C. List the different possible amounts of money, in dollars, Lana could have.

different possible amounts:

672731



1Algebra I MODULE 1





A1.1.3—Linear Inequalities


A1.1.3.1—Write, solve, and/or graph linear inequalities using various methods.

Scoring Guide

Score Description

4Demonstrates a thorough understanding of writing and/or solving a system of linear inequalities and interpreting solutions to problems in the context of the problem situation by correctly solving problems and clearly explaining procedures.

3Demonstrates a general understanding of writing and/or solving a system of linear inequalities and interpreting solutions to problems in the context of the problem situation by correctly solving problems and clearly explaining procedures with only minor errors or omissions.

2Demonstrates a partial understanding of writing and/or solving a system of linear inequalities and interpreting solutions to problems in the context of the problem situation by correctly performing a significant portion of the required task.

1 Demonstrates minimal understanding of writing and/or solving a system of linear inequalities and interpreting solutions to problems in the context of the problem situation.



1Algebra I MODULE 1


Score Description




1 Student earns 1 point.

0 Response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.


Part A (2 points):

2 points for correct answer OR1 point for correct half of compound inequality OR1 point for correct inequalities joined by “or”

What? Why?

38 ≤ 2x + 4 < 56

OR

2x + 4 ≥ 38 and 2x + 4 < 56

OR

17 ≤ x < 26

OR

x ≥ 17 and x < 26

OR equivalent

Part B (1 point):

1 point for correct answer

What? Why?

($)17

[note: carry over any error from part A]


1Algebra I MODULE 1

Part C (1 point):


What? Why?

($)17, ($)18, ($)19, ($)20, ($)21, ($)22, ($)23, ($)24, ($)25

[note: carry over any error from part A]


1Algebra I MODULE 1



1Algebra I MODULE 1

STUDENT RESPONSE






$


The response provides a correct answer (equivalent compound inequality).

The response provides a correct answer.


1Algebra I MODULE 1








1Algebra I MODULE 1

STUDENT RESPONSE


PARTS A, B, AND C

Que

stio

n 14

The

resp

onse

pro

vide

s one

cor

rect

hal

f of

the

corr

ect c

ompo

und

equa

lity

(2

x + 4

< 5

6).

The

resp

onse

pro

vide

s a c

orre

ct a

nsw

er.

The

resp

onse

pro

vide

s a c

orre

ct a

nsw

er.


1Algebra I MODULE 1



1Algebra I MODULE 1

STUDENT RESPONSE






$


The response provides an incorrect answer.



1Algebra I MODULE 1








1Algebra I MODULE 1

STUDENT RESPONSE


PARTS A, B, AND C

Que

stio

n 14

The

resp

onse

pro

vide

s an

inco

rrec

t an

swer

. Bot

h in

equa

lity

signs

are

in

corr

ect.

The

resp

onse

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s a c

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er.

The

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pro

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s an

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t ans

wer

.


1Algebra I MODULE 1



1Algebra I MODULE 1

STUDENT RESPONSE






$





1Algebra I MODULE 1








1Algebra I MODULE 1

ALGEBRA I MODULE 1—SUMMARY DATA

MULTIPLE-CHOICE

Sample Number Alignment Answer Key

Depth of Knowledge

p -values A

p -values B

p -values C

p -values D

1 A1.1.1.1.1 C 1 14% 17% 60% 9%

2 A1.1.1.3.1 B 1 11% 62% 13% 14%

3 A1.1.1.5.1 A 2 41% 31% 17% 11%

4 A1.1.1.5.3 C 1 11% 22% 51% 16%

5 A1.1.2.1.1 D 2 7% 39% 4% 50%

6 A1.1.2.1.3 C 2 14% 4% 80% 2%

7 A1.1.2.2.1 D 2 5% 10% 12% 73%

8 A1.1.2.2.2 A 2 77% 5% 12% 6%

9 A1.1.3.1.2 B 1 24% 46% 17% 13%

10 A1.1.3.1.3 D 2 22% 20% 18% 40%

11 A1.1.3.2.1 B 2 15% 47% 14% 24%

12 A1.1.3.2.2 A 2 66% 13% 13% 8%

CONSTRUCTED-RESPONSE

Sample Number Alignment Points

Depth of Knowledge Mean Score

13 A1.1.2 4 2 1.58

14 A1.1.3 4 2 1.00


1Algebra I MODULE 1



2Algebra I MODULE 2

ALGEBRA I MODULE 2Multiple-Choice Items

1. Chef Bailey measured the internal temperature of a whole chicken during the first 60 minutes of cooking time. The pattern in the temperatures she measured is shown in the table below.

Chicken Temperatures

Cooking Time (minutes) 15 30 45 60

Temperature (°F) 80 100 120 140

The pattern continues. Which graph best represents the pattern?

A.

50 60 70 80403020100

20

120100

40

140

60

160

80


Cooking Time(minutes)

Tem

pera

ture

(°F)

B.

50 60 70 80403020100

20

120100

40

140

60

160

80



Tem

pera

ture

(°F)

C.

50 60 70 80403020100

20

120100

40

140

60

160

80



Tem

pera

ture

(°F)

D.

50 60 70 80403020100

20

120100

40

140

60

160

80



Tem

pera

ture

(°F)

657752


2Algebra I MODULE 2

Item Information


Answer Key B


p-value A 7%


p-value C 7%

p-value D 14%

Option Annotations A student could determine the correct answer, option B, by using the pattern

in the table to determine the rate of change ( 4 } 3 ) and the initial temperature

(60°F).

A student could arrive at an incorrect answer by incorrectly identifying which value to use as the initial temperature. For example, a student could arrive at option D by using the first temperature from the table as the initial temperature.


2Algebra I MODULE 2

2. Which set of ordered pairs is a function?

A. {( ̄ 10, 4), ( ̄ 8, 3), ( ̄ 8, 2), ( ̄ 4, 1)}

B. {( ̄ 2, 4), (0, 4), (2, 4), (2, 6)}

C. {(1, 5), (1, 6), (2, 7), (3, 8)}

D. {( ̄ 1, 1), (0, 0), (1, 1), (2, 2)}703977

Item Information


Answer Key D


p-value A 10%

p-value B 9%

p-value C 17%


Option Annotations A student could determine the correct answer, option D, by selecting the answer that shows each x -value with only one y -value.

A student could arrive at an incorrect answer by failing to notice that there are different y -values for the same x -value. For example, a student could arrive at option C by not noticing that the first and second points have different y -values for the same x -value.


2Algebra I MODULE 2

3. Laura drove her car on three trips. She began each trip with a full tank of fuel in her car. The table below shows the relation between the distance driven on each trip and the amount of fuel remaining in the car’s fuel tank at the end of the trip.

Laura’s Trips

Distance Driven (miles)

Amount of Fuel Remaining (gallons)

60 15

160 10

200 8

What is the range of the relation in the table?

A. {8, 10, 15}

B. {60, 160, 200}

C. {all whole numbers from 8 through 15}

D. {all whole numbers from 60 through 200}678738

Item Information


Answer Key A



p-value B 20%

p-value C 17%

p-value D 12%

Option Annotations A student could determine the correct answer, option A, by selecting the dependent values (amount of fuel remaining) shown in the table.

A student could arrive at an incorrect answer by identifying the domain instead of the range or by including all whole number values between the given numbers. For example, a student could arrive at option B by identifying the domain instead of the range.


2Algebra I MODULE 2

4. Paul inherited a stamp collection. Since receiving the collection, Paul has gone to the store and bought the same number of new stamps each week to add to his collection. The equation shown below can be used to determine the number of stamps (y ) in Paul’s stamp collection x weeks after he inherited the stamps.

y = 3x + 40

Based on the equation, which statement is true?

A. The stamp collection had 3 stamps in it when Paul inherited it.

B. So far, Paul has purchased 40 additional stamps for the collection.

C. Since inheriting the collection, Paul has bought 3 new stamps each week.

D. Six weeks after he inherited the collection, Paul’s stamp collection contains 18 stamps.673951

Item Information


Answer Key C


p-value A 5%

p-value B 17%


p-value D 4%

Option Annotations A student could determine the correct answer, option C, by interpreting the slope (3) as the number of new stamps Paul bought each week.

A student could arrive at an incorrect answer by misinterpreting what the values in the equation represent. For example, a student could arrive at option B by considering that the y -intercept represents additional records.



2Algebra I MODULE 2



2Algebra I MODULE 2

5. A function of x is graphed on the coordinate plane below.

x

y

2 4 6 8–2–4–6–8

–4–6–8

–2

2468

Which table represents the function?

A. x y–8–6–4–2

1915117

B. x y–8–6–4–2

50382614

C. x y–8–6–4–2

22181410

D. x y–8–6–4–2

30241812

605117


2Algebra I MODULE 2

Item Information


Answer Key C


p-value A 25%

p-value B 12%


p-value D 14%

Option Annotations A student could determine the correct answer, option C, response by determining which table has the same rate of change ( ̄3) and y -intercept (6) as the given function.

A student could arrive at an incorrect answer by incorrectly using the intercepts. For example, a student could arrive at option A by using the x -intercept as the y -intercept ( y = ˉ2x + 3).


2Algebra I MODULE 2

6. A caterer uses 4 pans of lasagna to serve 30 people. At this rate, how many pans of lasagna does the caterer use to serve 390 people?

A. 13

B. 52

C. 90

D. 98702537

Item Information


Answer Key B


p-value A 16%


p-value C 4%

p-value D 11%

Option Annotations A student could determine the correct answer, option B, by dividing 4 by 30 to determine the rate per person and then multiplying the rate by 390.

A student could arrive at an incorrect answer by incorrectly determining and/or applying the rate. For example, a student could arrive at option A by dividing 390 by 30.


2Algebra I MODULE 2

7. Which linear equation has the points ( 1 } 2 , 3 } 4 ) and (4, 3) as solutions?

A. 9x – 14y = ˉ6

B. 9x + 14y = 78

C. y – 3 = 14 } 9 (x – 4)

D. y – 4 = 9 } 14

(x – 3)

681814

Item Information


Answer Key A



p-value B 17%

p-value C 21%

p-value D 13%

Option Annotations A student could determine the correct answer, option A, by determining the

slope using the slope formula (m = (3 – 3 }

4 ) }

(4 – 1 } 2 ) =

( 9 } 4 ) }

( 7 } 2 ) = 9 }

14 ) , substituting the slope

and one of the points into the point-slope formula, and then identifying an

equivalent equation.

A student could arrive at an incorrect answer by testing only one of the points,

inverting the slope, or switching the x -values and y -values. For example, a

student could arrive at option C by substituting the inverse of the slope ( 14 } 9 )

and the point (4, 3) into the point-slope formula.


2Algebra I MODULE 2

8. Martha earns money sewing curtains. She charges a flat fee to meet with a customer and take window measurements and an hourly rate to sew the curtains. The graph below shows the relationship between the time, in hours, Martha works on a sewing project and the total amount, in dollars, she charges.

y

x2 4 6 8 910 3 5

Time (hours)

Martha’s Sewing Charges

Tota

l Cha

rges

($)

7

40

80

20

60

100120

What is the hourly rate that Martha charges for sewing curtains?

A. $10.00

B. $12.50

C. $15.00

D. $20.00702478

Item Information


Answer Key A



p-value B 6%

p-value C 8%

p-value D 23%

Option Annotations A student could determine the correct answer, option A, by using two points

on the graph to determine the slope (e.g., m = (100 – 20)

} (8 – 0)

= 80 } 8 = 10).

A student could arrive at an incorrect answer by using a point on the graph to determine a proportional rate. For example, a student could arrive at option D by confusing the hourly rate with the flat fee or by using the point (2, 40) and dividing 40 by 2 to determine the hourly rate.


2Algebra I MODULE 2

9. A data set contains student test scores.

• The median test score is 75 points. • The third quartile value is 85 points. • The range of the test scores is 40 points.

Which statement about the test scores in the data set is most likely true?

A. The lowest test score is 45 points.

B. The highest test score is 95 points.

C. About 25% of the test scores are less than 55 points.

D. About 25% of the test scores are between 75 and 85 points.702481

Item Information


Answer Key D


p-value A 11%

p-value B 13%

p-value C 15%


Option Annotations A student could determine the correct answer, option D, by recognizing that about 25% of the data will be between the median and third quartile values.

A student could arrive at an incorrect answer by confusing the quartile values, confusing the range and the interquartile range, and/or assuming symmetry in the data set. For example, a student could arrive at option C by confusing the range and the interquartile range, assuming symmetry in the data set, and subtracting 20 from 75.


2Algebra I MODULE 2

10. The scatter plot below shows nine points from a data set.

0 1 2 3 4 5 6 7 8 9 10x

1.22.43.64.86.07.28.49.6

10.812.0

y

The equation of the line of best fit for the nine points is determined. Then, three more points are added to the scatter plot, but the equation of the original line of best fit remains unchanged. Which three ordered pairs are most likely the added data points?

A. (4, 4), (5, 5), (6, 6)

B. (4, 10), (4, 11), (4, 12)

C. (8, 9), (8, 10), (8, 11)

D. (10, 10), (10, 11), (10, 12)696806


2Algebra I MODULE 2

Item Information


Answer Key B


p-value A 12%


p-value C 9%

p-value D 6%

Option Annotations A student could determine the correct answer, option B, by either identifying a correct line of best fit (e.g., y = 3x – 1) and identifying a set of points that fits that line or recognizing a pattern formed by the given set of points and extending that pattern.

A student could arrive at an incorrect answer by misinterpreting the pattern created by the data in the scatter plot. For example, a student could arrive at option A by noticing the y -values all increase by 1 but not considering the x -values repeat for each set of three data points.


2Algebra I MODULE 2

11. The scatter plot below shows the relationship between the age of a house and the number of days it takes for the house to be sold after being listed for sale.

203040506070

y

x10

0 5 10 15 20

Age of House (years)

House Sales

Num

ber o

f Day

s

25 30 35 40

The equation y = 0.95x + 17.56 describes the line of best fit for the scatter plot. Based on the equation, which value is most likely the number of days it takes for a 60-year-old house to be sold after being listed for sale?

A. 45

B. 70

C. 75

D. 83696806

Item Information


Answer Key C


p-value A 11%

p-value B 17%


p-value D 13%

Option Annotations A student could determine the correct answer, option C, by correctly substituting 60 in for x , solving for y , and then identifying the value closest to y = 74.56.

A student could arrive at an incorrect answer by incorrectly using the graph or the equation of the given line of best fit. For example, a student could arrive at option B by using the greatest value shown on the y -axis.


2Algebra I MODULE 2

12. There are 28 students whose last names begin with the letters G, H, J, or K. Information about the probability of randomly selecting one of these students is listed below.

• probability of selecting a student whose last name begins with G: 1 } 7

• probability of selecting a student whose last name begins with G or H: 5 } 14

How many of these students have a last name that begins with H?

A. 4

B. 5

C. 6

D. 7702502

Item Information


Answer Key C


p-value A 30%

p-value B 16%


p-value D 16%

Option Annotations A student could determine the correct answer, option C, by subtracting 1 } 7

from 5 } 14

and then multiplying that value by 28.

A student could arrive at an incorrect answer by incorrectly applying the probabilities. For example, a student could arrive at option A by determining the difference in the numerators: 5 – 1.


2Algebra I MODULE 2


13. Javier has a website on which he posts photos and videos. The day he started the website, he posted 12 photos and no videos. For each day after he started the website, he posts 4 new photos and 1 new video.

A. Complete the table below to show the total number of photos and the total number of videos that are on the website based on the number of days since Javier started the website.

Photos and Videos on Javier’s Website

Days since Starting Website

Photos on Website

Videos on Website

0 12 0

1 16 1

2

3

B. Write the rate of change in the total number of photos on the website each day since Javier started the website.

rate of change:

C. Write a linear equation to show the relationship between the total number of videos (v ) on the website and the number of days (x ) since Javier started the website.

equation:



2Algebra I MODULE 2


D. Draw a line on the coordinate grid to show the relationship between the combined number of photos and videos (y ) on the website and the number of days (x ) since Javier started the website.



Num

ber o

f Pho

tos

and

Vide

os 403632282420161284

10 2 3 4 65 7 8

y

x

701634



2Algebra I MODULE 2





A1.2.1—Functions


A1.2.1.2—Interpret and/or use linear functions and their equations, graphs, or tables.

Scoring Guide

Score Description

4 The student demonstrates a thorough understanding of functions by correctly solving problems with clear and complete procedures and explanations when required.

3 The student demonstrates a general understanding of functions by solving problems and providing procedures and explanations with only minor errors or omissions.

2 The student demonstrates a partial understanding of functions by providing a portion of the correct problem solving, procedures, and explanations.

1 The student demonstrates a minimal understanding of functions.



Score Description




1Student earns 0.5–1.5 points. OR Student demonstrates minimal understanding of functions.

0 The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.


2Algebra I MODULE 2


Part A (1 point):


What? Why?

Part B (1 point):


What? Why?

4

Part C (1 point):


What? Why?

v = x


2Algebra I MODULE 2

Part D (1 point):


What? Why?

Answers may vary. The solid line below represents the equation y = 5x + 12. Students must draw a reasonably straight line that passes through (0, 12), 2 < x < 3 for y = 24, and 24 < y < 28 for x = 3 (see shading below). Note: line cannot pass through (2, 24), (3, 24), or (3, 28).


2Algebra I MODULE 2

STUDENT RESPONSE


PART A

Que

stio

n 13

Page

1 o

f 3

The

resp

onse

pro

vide

s a c

orre

ct a

nsw

er.


2Algebra I MODULE 2

STUDENT RESPONSE

PARTS B AND C

Q

uest

ion

13

Pa

ge 2

of

3

The

resp

onse

pro

vide

s a c

orre

ct

answ

er.

The

resp

onse

pro

vide

s a c

orre

ct

answ

er.


2Algebra I MODULE 2

STUDENT RESPONSE

PART D

Q

uest

ion

13

Pa

ge 3

of

3

The

resp

onse

pro

vide

s a

corr

ectly

plo

tted

line

.


2Algebra I MODULE 2

STUDENT RESPONSE






Photos on Website

Videos on Website

0 12 0

1 16 1

2

3


rate of change:


equation:






2Algebra I MODULE 2





Num

ber o

f Pho

tos

and

Vide

os 403632282420161284

10 2 3 4 65 7 8

y

x


The response provides a correctly plotted line.


2Algebra I MODULE 2

STUDENT RESPONSE


PART A

Que

stio

n 13

Page

1 o

f 3

The

resp

onse

pro

vide

s a c

orre

ct a

nsw

er.


2Algebra I MODULE 2

STUDENT RESPONSE

PARTS B AND C

Q

uest

ion

13

Pa

ge 2

of

3

The

resp

onse

pro

vide

s an

inco

rrec

t an

swer

.

The

resp

onse

pro

vide

s a c

orre

ct

answ

er.


2Algebra I MODULE 2

STUDENT RESPONSE

PART D

Q

uest

ion

13

Pa

ge 3

of

3

The

resp

onse

pro

vide

s an

inco

rrec

tly p

lott

ed li

ne.



2Algebra I MODULE 2



2Algebra I MODULE 2

STUDENT RESPONSE






Photos on Website

Videos on Website

0 12 0

1 16 1

2

3


rate of change:


equation:






2Algebra I MODULE 2





Num

ber o

f Pho

tos

and

Vide

os 403632282420161284

10 2 3 4 65 7 8

y

x


The response provides an incorrectly plotted line.


2Algebra I MODULE 2

STUDENT RESPONSE


PART A

Que

stio

n 13

Page

1 o

f 3

The

resp

onse

pro

vide

s an

inco

rrec

t an

swer

.


2Algebra I MODULE 2

STUDENT RESPONSE

PARTS B AND C

Q

uest

ion

13

Pa

ge 2

of

3

The

resp

onse

pro

vide

s an

inco

rrec

t an

swer

.

The

resp

onse

pro

vide

s an

inco

rrec

t an

swer

.


2Algebra I MODULE 2

STUDENT RESPONSE

PART D

Q

uest

ion

13

Pa

ge 3

of

3

The

resp

onse

pro

vide

s an

inco

rrec

tly p

lott

ed li

ne.



2Algebra I MODULE 2



2Algebra I MODULE 2


14. Points J and K lie on the same line, as shown on the coordinate plane below.

x

y

2 4 6

K(6, 5)

J(3, 3.5)

– 4– 6

– 2

246

– 2– 4– 6

A. What is the slope of the line passing through points J and K? Show or explain all your work.



2Algebra I MODULE 2


B. Write the equation of the line passing through points J and K. Show or explain all your work.

Points L and M are added to the coordinate plane. The slope of is equal to the

slope of .

C. Describe two ways the lines could be related.



2Algebra I MODULE 2





A1.2.2—Coordinate Geometry


A1.2.2.1—Describe, compute, and/or use the rate of change (slope) of a line.

Scoring Guide

Score Description

4 The student demonstrates a thorough understanding of coordinate geometry by correctly solving problems with clear and complete procedures and explanations when required.

3 The student demonstrates a general understanding of coordinate geometry by solving problems and providing procedures and explanations with only minor errors or omissions.

2 The student demonstrates a partial understanding of coordinate geometry by providing a portion of the correct problem solving, procedures, and explanations.

1 The student demonstrates a minimal understanding of coordinate geometry.



Score Description




1Student earns 0.5–1.5 points. OR Student demonstrates minimal understanding of coordinate geometry.

0 The response is incorrect or contains some correct work that is irrelevant to the skill or concept being measured.


2Algebra I MODULE 2


Part A (1 point):

1 } 2 point for correct answer

1 } 2 point for complete support

What? Why?

1 } 2

OR

0.5

Sample Work:

5 – 3.5 } 6 – 3

= 1.5 } 3 = 1 }

2

OR

Sample Explanation:

To determine the slope, I found the difference in the y -coordinates and divided that

by the difference in the x -coordinates. The difference in the y -coordinates is

5 – 3.5 = 1.5. The difference in the x -coordinates is 6 – 3 = 3. So the slope is

1.5 divided by 3, which is 1 } 2 (or 0.5).


2Algebra I MODULE 2

Part B (1 point):

1 } 2

point for correct answer

1 } 2

point for complete support

What? Why?

y = 1 } 2

x + 2

OR equivalent

Note: carry-through possible based on part A

Sample Work:

y – 5 = 1 } 2 (x – 6)

y = 1 } 2 x – 3 + 5

y = 1 } 2 x + 2

OR

Sample Explanation:

To determine the equation, I used the point-slope formula:

y – y 1 = m(x – x 1). Since the slope is 1 } 2 (part A), I substituted that for m. I picked

point K (6, 5) to substitute in for x 1 and y 1. I then simplified the equation so it

would be in slope-intercept form.

Part C (2 points):

1 point for each correct answer

What? Why?

Line JK and line LM could be parallel lines

OR equivalent

AND

Line JK and line LM could be the same line (or collinear lines)

OR equivalent



2Algebra I MODULE 2



2Algebra I MODULE 2

STUDENT RESPONSE



x

y

2 4 6

K(6, 5)

J(3, 3.5)

– 4– 6

– 2

246

– 2– 4– 6



The student has provided a correct answer and complete support.


2Algebra I MODULE 2




slope of .



The student has provided a correct equation and complete support.

The student has provided two correct answers.


2Algebra I MODULE 2

STUDENT RESPONSE


PART A

Que

stio

n 14

Page

1 o

f 2

The

stud

ent h

as p

rovi

ded

a co

rrec

t an

swer

and

com

plet

e su

ppor

t.


2Algebra I MODULE 2

STUDENT RESPONSE

PARTS B AND C

Que

stio

n 14

Page

2 o

f 2

The

stud

ent h

as p

rovi

ded

a co

rrec

t eq

uatio

n an

d co

mpl

ete

supp

ort.

The

stud

ent h

as p

rovi

ded

one

corr

ect a

nsw

er (“

If th

ey fa

ll on

the

sam

e lin

e” ).


2Algebra I MODULE 2

STUDENT RESPONSE



x

y

2 4 6

K(6, 5)

J(3, 3.5)

– 4– 6

– 2

246

– 2– 4– 6



The student has provided a correct answer and complete support.


2Algebra I MODULE 2




slope of .



The student has provided one correct answer (“They could be parallel to one another” ).

The student has provided a correct equation but no support.


2Algebra I MODULE 2

STUDENT RESPONSE


PART A

Que

stio

n 14

Page

1 o

f 2

The

stud

ent h

as p

rovi

ded

a co

rrec

t ans

wer

but

in

com

plet

e su

ppor

t. (T

he e

xpla

natio

n do

es n

ot

desc

ribe

how

the

num

bers

resu

lt in

a sl

ope

of 1

/2.)


2Algebra I MODULE 2

STUDENT RESPONSE

PARTS B AND C

Que

stio

n 14

Page

2 o

f 2

The

stud

ent h

as p

rovi

ded

an in

corr

ect

equa

tion

and

no su

ppor

t.

The

stud

ent h

as p

rovi

ded

no c

orre

ct

answ

ers.


2Algebra I MODULE 2

STUDENT RESPONSE



x

y

2 4 6

K(6, 5)

J(3, 3.5)

– 4– 6

– 2

246

– 2– 4– 6



The student has provided an incorrect answer and no support.


2Algebra I MODULE 2




slope of .



The student has provided an incorrect equation of the line and no support.

The student has provided no correct answers.


2Algebra I MODULE 2

ALGEBRA I MODULE 2—SUMMARY DATA

MULTIPLE-CHOICE

Sample Number Alignment Answer Key

Depth of Knowledge

p -values A

p -values B

p -values C

p -values D

1 A1.2.1.1.1 B 2 7% 72% 7% 14%

2 A1.2.1.1.2 D 1 10% 9% 17% 64%

3 A1.2.1.1.3 A 1 51% 20% 17% 12%

4 A1.2.1.2.1 C 2 5% 17% 74% 4%

5 A1.2.1.2.2 C 2 25% 12% 49% 14%

6 A1.2.2.1.1 B 2 16% 69% 4% 11%

7 A1.2.2.1.3 A 1 49% 17% 21% 13%

8 A1.2.2.1.4 A 2 63% 6% 8% 23%

9 A1.2.3.1.1 D 2 11% 13% 15% 61%

10 A1.2.3.2.2 B 2 12% 73% 9% 6%

11 A1.2.3.2.3 C 2 11% 17% 59% 13%

12 A1.2.3.3.1 C 2 30% 16% 38% 16%

CONSTRUCTED-RESPONSE

Sample Number Alignment Points

Depth of Knowledge Mean Score

13 A1.2.1 4 2 2.23

14 A1.2.2 4 2 1.66



2Algebra I MODULE 2


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